You can look in the Australian Electoral Rolls (available on http://www.ancestry.com.au) for May and Cornelius O'Neill for the years 1960 through 1980 to see if there are any children still living at home after they reached voting age and registered to vote.
Additionally you can search the Australian newspapers at http://trove.nla.gov.au/newspaper for births, deaths, marriages, obituaries, in memoria, news articles, etc for mention of May and Cornelius.